Space of modular forms of level 1088, weight 2, and Character 1088.o

• Label: 1088.2.o
• Level: $1088$
• Weight: $2$
• Character orbit: 1088.o
• Rep. character: $\chi_{1088}(769,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $68$
• Newform subspaces: $23$
• Sturm bound: $288$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1088 = 2^{6} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1088.o (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 23 \)
Sturm bound:			\(288\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1088, [\chi])\).

	Total	New	Old
Modular forms	312	76	236
Cusp forms	264	68	196
Eisenstein series	48	8	40

Trace form

\( 68 q + 4 q^{5} + 8 q^{13} - 12 q^{17} + 8 q^{21} + 4 q^{29} - 8 q^{33} + 4 q^{37} - 12 q^{41} - 28 q^{45} + 24 q^{57} + 36 q^{61} - 40 q^{65} - 56 q^{69} - 12 q^{73} - 12 q^{81} + 4 q^{85} - 8 q^{89} - 12 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1088, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1088.2.o.a	$1088$	$2$	1088.o	17.c	$4$	$2$	$1$	$8.688$	\(\Q(\sqrt{-1}) \)	None					544.2.o.a	$2$	$1$	\(0\)	\(-4\)	\(2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2 i-2)q^{3}+(i+1)q^{5}+(-2 i+2)q^{7}+\cdots\)
1088.2.o.b	$1088$	$2$	1088.o	17.c	$4$	$2$	$1$	$8.688$	\(\Q(\sqrt{-1}) \)	None					136.2.k.d	$2$	$0$	\(0\)	\(-4\)	\(2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2 i-2)q^{3}+(i+1)q^{5}+(-2 i+2)q^{7}+\cdots\)
1088.2.o.c	$1088$	$2$	1088.o	17.c	$4$	$2$	$1$	$8.688$	\(\Q(\sqrt{-1}) \)	None					136.2.k.b	$2$	$0$	\(0\)	\(-2\)	\(-4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i-1)q^{3}+(-2 i-2)q^{5}+(2 i-2)q^{7}+\cdots\)
1088.2.o.d	$1088$	$2$	1088.o	17.c	$4$	$2$	$1$	$8.688$	\(\Q(\sqrt{-1}) \)	None					34.2.c.a	$2$	$0$	\(0\)	\(-2\)	\(-4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i-1)q^{3}+(-2 i-2)q^{5}+(-2 i+2)q^{7}+\cdots\)
1088.2.o.e	$1088$	$2$	1088.o	17.c	$4$	$2$	$1$	$8.688$	\(\Q(\sqrt{-1}) \)	None					136.2.k.c	$2$	$1$	\(0\)	\(-2\)	\(-2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i-1)q^{3}+(-i-1)q^{5}+(i-1)q^{7}+\cdots\)
1088.2.o.f	$1088$	$2$	1088.o	17.c	$4$	$2$	$1$	$8.688$	\(\Q(\sqrt{-1}) \)	None					544.2.o.b	$2$	$0$	\(0\)	\(-2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i-1)q^{3}+(2 i+2)q^{5}-i q^{9}+\cdots\)
1088.2.o.g	$1088$	$2$	1088.o	17.c	$4$	$2$	$1$	$8.688$	\(\Q(\sqrt{-1}) \)	None					136.2.k.a	$2$	$0$	\(0\)	\(-2\)	\(6\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-i-1)q^{3}+(3 i+3)q^{5}+(-3 i+3)q^{7}+\cdots\)
1088.2.o.h	$1088$	$2$	1088.o	17.c	$4$	$2$	$1$	$8.688$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)					544.2.o.d	$4$	$1$	\(0\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-3 i-3)q^{5}-3 i q^{9}-4 q^{13}+\cdots\)
1088.2.o.i	$1088$	$2$	1088.o	17.c	$4$	$2$	$1$	$8.688$	\(\Q(\sqrt{-1}) \)	None					34.2.c.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i+1)q^{5}-3 i q^{9}+(4 i-4)q^{11}+\cdots\)
1088.2.o.j	$1088$	$2$	1088.o	17.c	$4$	$2$	$1$	$8.688$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)					544.2.o.c	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(i+1)q^{5}-3 i q^{9}+4 q^{13}+(-4 i-1)q^{17}+\cdots\)
1088.2.o.k	$1088$	$2$	1088.o	17.c	$4$	$2$	$1$	$8.688$	\(\Q(\sqrt{-1}) \)	None					34.2.c.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i+1)q^{5}-3 i q^{9}+(-4 i+4)q^{11}+\cdots\)
1088.2.o.l	$1088$	$2$	1088.o	17.c	$4$	$2$	$1$	$8.688$	\(\Q(\sqrt{-1}) \)	None					34.2.c.a	$2$	$0$	\(0\)	\(2\)	\(-4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i+1)q^{3}+(-2 i-2)q^{5}+(2 i-2)q^{7}+\cdots\)
1088.2.o.m	$1088$	$2$	1088.o	17.c	$4$	$2$	$1$	$8.688$	\(\Q(\sqrt{-1}) \)	None					136.2.k.b	$2$	$0$	\(0\)	\(2\)	\(-4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i+1)q^{3}+(-2 i-2)q^{5}+(-2 i+2)q^{7}+\cdots\)
1088.2.o.n	$1088$	$2$	1088.o	17.c	$4$	$2$	$1$	$8.688$	\(\Q(\sqrt{-1}) \)	None					136.2.k.c	$2$	$0$	\(0\)	\(2\)	\(-2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i+1)q^{3}+(-i-1)q^{5}+(-i+1)q^{7}+\cdots\)
1088.2.o.o	$1088$	$2$	1088.o	17.c	$4$	$2$	$1$	$8.688$	\(\Q(\sqrt{-1}) \)	None					544.2.o.b	$2$	$0$	\(0\)	\(2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i+1)q^{3}+(2 i+2)q^{5}-i q^{9}+\cdots\)
1088.2.o.p	$1088$	$2$	1088.o	17.c	$4$	$2$	$1$	$8.688$	\(\Q(\sqrt{-1}) \)	None					136.2.k.a	$2$	$0$	\(0\)	\(2\)	\(6\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(i+1)q^{3}+(3 i+3)q^{5}+(3 i-3)q^{7}+\cdots\)
1088.2.o.q	$1088$	$2$	1088.o	17.c	$4$	$2$	$1$	$8.688$	\(\Q(\sqrt{-1}) \)	None					136.2.k.d	$2$	$0$	\(0\)	\(4\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2 i+2)q^{3}+(i+1)q^{5}+(2 i-2)q^{7}+\cdots\)
1088.2.o.r	$1088$	$2$	1088.o	17.c	$4$	$2$	$1$	$8.688$	\(\Q(\sqrt{-1}) \)	None					544.2.o.a	$2$	$0$	\(0\)	\(4\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2 i+2)q^{3}+(i+1)q^{5}+(2 i-2)q^{7}+\cdots\)
1088.2.o.s	$1088$	$2$	1088.o	17.c	$4$	$4$	$2$	$8.688$	\(\Q(i, \sqrt{13})\)	None					68.2.e.a	$2$	$0$	\(0\)	\(-2\)	\(4\)	\(-2\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\beta _{2})q^{3}+(1+\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1088.2.o.t	$1088$	$2$	1088.o	17.c	$4$	$4$	$2$	$8.688$	\(\Q(i, \sqrt{13})\)	None					68.2.e.a	$2$	$0$	\(0\)	\(2\)	\(4\)	\(2\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{1})q^{5}+(1+\cdots)q^{7}+\cdots\)
1088.2.o.u	$1088$	$2$	1088.o	17.c	$4$	$6$	$3$	$8.688$	6.0.419904.1	None					544.2.o.g	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{4}q^{3}+(-1-\beta _{2})q^{5}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
1088.2.o.v	$1088$	$2$	1088.o	17.c	$4$	$6$	$3$	$8.688$	6.0.419904.1	None					544.2.o.g	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{3}q^{3}+(-1-\beta _{1})q^{5}+(\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
1088.2.o.w	$1088$	$2$	1088.o	17.c	$4$	$12$	$6$	$8.688$	12.0.\(\cdots\).2	None			✓		544.2.o.i	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{3}q^{3}+\beta _{9}q^{5}+(-\beta _{1}-\beta _{5})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1088, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1088, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(272, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(544, [\chi])\)\(^{\oplus 2}\)